Where can I get the "Cut" HM, and how do I reteach an HM to a different pokemon?

I taught some random Woober "Flash", but I don't want him to have it as I'd rather set up an HM Slave such as Psyduck with it as well as surf, whirlpool and another move.

you get cut in Ilex Forest

Only way to remove HMs ( I assume that is what you mean by reteach ), is to go to Blackthorn city

And also Flash isnt an HM in these new games.

this lol an hms can be used more then once